1FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007Lecture 3 – Univariate and BivariateProbabilityAgendaÉSimulation of Exponential Random VariableÉSimulation of Uniform Random VariableÉSimulation of Gumbel Random VariableÉNon-Parametric Density ModelsÉBivariate Continuous DistributionsÉMultivariate Continuous DistributionsÉBivariate Discrete DistributionsÉMultivariate Discrete Distributions2FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007Simulation of Exponential Random VariableWe use the inversion of CDF transformation from Lecture 2 to generate sample random variables or deviates that are independent and identically distributed (i.i.d.) according the following exponential distribution()()()1expXFxxHxλ⎡⎤=−−⎣⎦We define the following relationship()1XXFU−=3FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007Simulation of Exponential Random Variable()()()()11expexp1log 1log 1UXXUXUXUλλλλ−=−−−=−−=−= −−Excel workbook file Class03a.xls contains the sample simulation. R workspace contains the corresponding simulation using R. Let’s estimate the mean and variance of an exponential random variable.
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